Least Common Multiple (LCM) of 177 and 47
The least common multiple (LCM) of 177 and 47 is 8319.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 177 and 47?
First, calculate the GCD of 177 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 47 = 3 remainder 36 |
| 2 | 47 ÷ 36 = 1 remainder 11 |
| 3 | 36 ÷ 11 = 3 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 124 | 22196 |
| 122 and 176 | 10736 |
| 188 and 93 | 17484 |
| 174 and 101 | 17574 |
| 54 and 145 | 7830 |